Plastic bags, such as plastic trash bags, are generally closed by means of a twist tie that is placed around the top of the bag after the bag is twisted to close it. Generally, the ties are provided in strips in the box in which the bags are sold. This type of tie is often hard to find after they have been removed from the box and, if the bag is full, the ties do not always hold the bag closed. Plastic key locks ties in which one end of the plastic tie strip is inserted through a key lock in the other end of the tie, are also used to achieve a closing of the bag. However, this type of tie is more expensive than the plain twist tie, and still are subject to being lost after they have been removed from the box. In an attempt to prevent the ties from being lost, a separate tie has been taped to each bag. However, this not only increases the cost of the bag, but also the ties are sometimes accidentally pulled off the bag when the bag is removed from the box or other package in which the bag is sold. Another type of closing means for plastic trash bags is a draw tape or the like extending through a hem at the top of the bag which will draw the top of the bag closed. One such bag of this type is disclosed in U.S. Pat. No. 4,558,463 to D. M. Boyd, issued Dec. 10, 1985, entitled HEM SEAL FOR DRAW TAPE TRASH BAG. Although this provides a good closure for the bag, it adds considerably to the cost of the bag. Therefore, it would be desirable to have a plastic trash bag which can be easily closed without any additional tie elements.